My last post on my quibbles about closure began by saying I’d explain why the issue isn’t merely terminological. Apparently, at 5 a.m., I forget by the end of the post what I said at the beginning…
Anyway, here’s the explanation.
The fundamental objection to widening the scope of what counts as a closure principle is that it makes a mockery of the debate about closure, making deniers of closure into defenders of such an implausible claim that no one would have thought to deny it. Here’s the principle critics of closure would have to deny:
there is some true epistemic principle that says that if take a set of propositions that are known by some person, there is some operation or process involving the deductive consequence relation in some way which is such that, when applied so as to produce some proposition q, implies that q falls into a favorable epistemic category (perhaps involving the concept of knowledge) for that person.
The favorable epistemic category might have to do with being in a position to know, which some would find unproblematic, but it might equally have to do with being justified in the way required for knowledge. To require of closure deniers the intention to undermine this principle is to raise the bar on their objections to such a height that it makes a mockery of the dispute. The proper stance to take on the dispute requires honoring enough of the mathematical home of the concept of closure so that the argument is about whether, in some way, an operation or process on a set of propositions having a certain property yields a result having that same property. Taken in this sense, there is an interesting dispute about whether there are any correct closure principles in epistemology; taken more broadly as in the last principle above, there has not been any such dispute.
On the other side of the fence here, it is true that critics of closure have given arguments that threaten both closure and non-closure epistemic principles. For example, Dretske’s disguised mule case threatens not only closure principles but also non-closure principles about being in a position to know that the object is not a cleverly disguised mule given that one knows that it is a zebra. People who’ve rejected the Dretske argument usually do so by citing some non-closure principle that it undermines, claiming that giving up that principle is just too much (the exception to this claim is John Hawthorne’s rejection in the Blackwell Debates volume). If they want to turn this response into a defense of closure, they need to do what Hawthorne attempts to do: formulate a closure principle that survives the example.